PDF-ASYMPTOTES OF RATIONAL FUNCTIONS

where polynomials By Joanna Gutt Lehr Pinnacle Learning Lab last updated 12010 VERTICAL ASYMPTOTE S x c A v ertical asymptote. A horizontal asymptote is a sp cial case of a slant asymptote recipe for find ing a horizontal asymptote of a rational function Let deg Nx the degree of a numerator and deg Dx the degree of a denominator deg Nx deg Dx deg Nx deg Dx deg Nx deg Dx In particular if the degree of is strictly less than that of d then the axis will be the horizontal asymptotea geometrical condition that can be expressed analytically by saying 0 as and as If the degree of is greater than or equal to the degree of lim lim 87221 lim lim 87221 A function has a horizontal asymptote of provided lim 1 or lim 87221 If the function is a rational function a polynomial divided by a polynomial then we have some shortcuts for 57356nding asymptotes Shortcut for V Describe the end behavior of:. Graph the function. Determine the interval(s) on which the function is increasing and on which it is decreasing. . Lesson 3-7 Graphs of Rational Functions. Objective: 1. To graph rational functions.. Precalculus. : Do Now. Graph the function below by hand. Be sure to factor the function, find the horizontal and vertical asymptotes, and the x and y-intercepts . Only use a graphing calculator at the very end to confirm your answer. REMEMBER FAITS!!. AII.7 e . 2009. Objectives:. Find the Vertical Asymptotes. Find the Horizontal Asymptotes. Rational . Functions . A rational function can have more than one . vertical asymptote. , but it can have at most one . A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . Optional Pre-Final Exam Review. 1 – Basic Algebra Review. 2 – Graphs & Equations of Lines. 3 – Solving Systems of Equations. 4 – Inequalities. 5 – Polynomials & Factoring. 6 – Rational Expressions & Functions. Evaluating Rational & Irrational Exponents. Graphing Exponential Functions . f(x) = a. x. Equations with . x. and . y. Interchanged. Applications of Exponential Functions. Use calculators to calculate graphing points. Functions. Defn. : . Rational . F. unction. A function in the form: .  . The functions . p. and . q. are polynomials.. The domain of a rational function is the set of all real numbers except those values that make the denominator, q(x), equal to zero.. What is a . rational . function?. Definition: . A function of the form . , where . and . are polynomials and . is not the zero polynomial.. What . is the most common form of the equation?.  . What does it look like?. Rational Equations and Functions Algebra II Chapter 8 This Slideshow was developed to accompany the textbook Larson Algebra 2 By Larson , R., Boswell, L., Kanold , T. D., & Stiff, L. 2011 Holt Writing Rational Functions Honors Algebra II Keeper Think Backwards!!! Example: Write a rational function f that has a vertical asymptote at , a horizontal asymptote and a zero at .   Example: Write a rational function g with vertical asymptotes at ECEN2260 R. W. Erickson1.Bode plots: basic rulesA Bode plot is a plot of phase of a transfer function or otherdecibels, and phase in are plotted vs. frequency, using semi-logarithmic axes. The magni